Question

Find the APY corresponding to the following nominal rate. 2​% compounded quarterly The APY is ____​%. ​(Type an integer or a decimal. Round to the nearest hundredth as​ needed.)

Answer 1

Answer:

2.02%.

Step-by-step explanation:

We are asked to find the Annual Percentage Yield (APY) for the nominal rate of 2% compounded quarterly.

We will use APY formula to solve our given problem.

$APY=(1+\frac{r}{n})^n-1$, where,

r = Stated annual interest rate in decimal form,

n = Number of times interest is compounded per year.

$2\%=\frac{2}{100}=0.02$

Compounded quarterly means that the value of n is 4.

$APY=(1+\frac{0.02}{4})^4-1$

$APY=(1+0.005)^4-1$

$APY=(1.005)^4-1$

$APY=1.020150500625-1$

$APY=0.020150500625$

Let us convert 0.020150500625 to percent as:

$0.020150500625\times 100\%=2.0150500625\%\approx 2.02\%$

Therefore, the required APY would be 2.02%.

$APY\approx 0.020150500625$